Tomographic image generation device and method, and recording medium

ABSTRACT

An image obtaining unit obtaining a plurality of projection images taken by imaging a subject with different radiation source positions. A pixel value projecting unit projects pixel values of the projection images on coordinate positions on a desired slice plane of the subject based on the positional relationship between the radiation source position with which each projection image is taken and the radiation detector, while preserving pixel values of the projection images. A pixel value calculating unit calculates a pixel value at each coordinate position of interest on the slice plane based on a plurality of pixel values of the projection images projected in a predetermined range relative to the coordinate position of interest on the slice plane to thereby generate a tomographic image of the slice plane.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. §119 to JapanesePatent Application No. 2014-190784, filed on Sep. 19, 2014 and JapaneseUnexamined Patent Application No. 2015-162559 filed on Aug. 20, 2015.Each of the above application(s) is hereby expressly incorporated byreference, in its entirety, into the present application.

BACKGROUND

The present disclosure relates to a tomographic image generation device,a tomographic image generation method and a tomographic image generationprogram for obtaining a plurality of projection images of a subject byimaging the subject with different radiation source positions, andgenerating a tomographic image from the projection images.

In recent years, in order to more closely observe an affected part ofthe body with a radiographic imaging apparatus using radiation, such asx-ray or γ-ray, tomosynthesis imaging has been proposed, in whichimaging is performed by applying radiation to the subject from differentradiation source positions by moving the radiation source, and the thusobtained projection images are added up to generate a tomographic imagein which a desired slice plane is emphasized. In the tomosynthesisimaging, a plurality of projection images are obtained by imaging asubject with different radiation source positions by moving theradiation source in parallel with the radiation detector or along acircular or ellipsoidal arc trajectory depending on characteristics ofthe imaging apparatus and necessary tomographic images, and theprojection images are reconstructed to generate a tomographic imageusing a simple reverse projection method, or a reverse projection methodsuch as a filter reverse projection method.

However, with the tomosynthesis imaging, angles at which the radiationcan be applied to the subject are limited, and there may be cases wherea tomographic image reconstructed from the projection images by areverse projection method, for example, includes an artifact which is avirtual image of a structure in an area of the tomographic image wherethe structure in the subject is not actually present. More specifically,the reverse projection may introduce an artifact of a structure in anarea where the structure is not actually present of the tomographicimage of a slice plane, which is different from a tomographic image of aslice plane where the structure is present. When such an artifact is toovisible, it is difficult to see a structure, such as a lesion, which isnecessary for diagnosis.

During the tomosynthesis imaging, the radiation is applied to thesubject at a plurality of times, and a radiation dose as low as possibleis used for each time to reduce the radiation exposure of the subject.However, a low radiation dose results in more quantum noise of radiationin the projection images obtained by the imaging, which in turn resultsin more visible noise in the reconstructed tomographic image.

Various techniques for reducing such an artifact or noise have beenproposed. For example, Japanese Unexamined Patent Publication No.2013-000261 (hereinafter, Patent Document 1) has proposed a techniquewhich involves: calculating a similarity between each pixel of areference projection image which is one of projection images and thecorresponding pixel of each of the other projection images, which pixelsare cumulatively added on the same position on a tomographic image;calculating a weighting factor for each pixel of the projection imagessuch that the weighting factor is greater when the similarity is higher;and reconstructing the tomographic image by calculating a cumulativeaddition of products calculated by multiplying each pixel value of eachprojection image with the corresponding weighting factor.

Besides the above-described technique, techniques called an algebraicreconstruction method or a iterative approximation reconstruction methodhave also been proposed. These techniques calculate a tomographic imagesuch that images formed by projecting the reconstructed tomographicimage agree with the actually taken projection images. These techniquesallow incorporating various mathematical models in the reconstruction,thereby allowing taking the artifact correction, the noise reduction,etc., into account to generate a tomographic image with suppressedartifacts and reduced noise.

However, the technique taught in Patent Document 1 and thereconstruction process such as the iterative approximationreconstruction method have a drawback that they require very longcalculation time. To address this problem, a technique for reducingartifacts while reducing the calculation time has been proposed, whichinvolves: generating a plurality of bandlimited images with differentfrequency response characteristics from projection images; performingnonlinear transformation on the bandlimited images such that portionsthat exceed a predetermined value of the bandlimited images becomesmall; adding up the bandlimited images after the nonlineartransformation to generate a plurality of transformed images; andreconstructing a tomographic image from the transformed images (seeJapanese Unexamined Patent Publication No. 2013-031641, hereinafter,Patent Document 2).

Japanese Unexamined Patent Publication Nos. 2005-013736 and11(1999)-339050 (hereinafter, Patent Documents 3 and 4, respectively)have proposed techniques to improve the calculation speed forreconstructing a tomographic image by setting the pixel size of thetomographic image the same as the pixel size of the radiation detectorregardless of the height of the slice plane.

SUMMARY

While the technique taught in Patent Document 2 allows reducingartifacts, it does not consider reducing noise. When it is attempted toreduce the calculation time, as taught in Patent Documents 2 to 4,sufficient reduction of artifacts may not be achieved. Further, in thetechniques taught in Patent Document 1 to 4, the pixel value at eachpixel position of interest on the tomographic image is calculated byadding up only the pixel values at pixel positions on the projectionimages corresponding to the pixel position of interest. Thereforeinfluence of noise or artifacts cannot be reduced sufficiently byperforming the weighting or the nonlinear transformation.

In view of the above-described circumstances, the present disclosure isdirected to improve the image quality of a tomographic image generatedfrom a plurality of projection images obtained by imaging, such astomosynthesis imaging, with different radiation source positions, whilereducing the calculation time.

An aspect of a tomographic image generation device according to thedisclosure comprises:

an image obtaining unit for obtaining a plurality of projection imagescorresponding to different radiation source positions, the projectionimages being taken by moving a radiation source relative to a detectingunit and applying radiation to a subject from the different radiationsource positions to which the radiation source is moved;

a pixel value projecting unit for projecting pixel values of theprojection images on coordinate positions on a desired slice plane ofthe subject based on a positional relationship between the radiationsource position with which each of the projection images is taken andthe detecting unit, while preserving the pixel values of the projectionimages; and

a pixel value calculating unit for calculating a pixel value at eachcoordinate position of interest on the slice plane based on a pluralityof pixel values of the projection images projected in a predeterminedrange relative to the coordinate position of interest on the slice planeto thereby generate a tomographic image of the slice plane.

The description “moving a radiation source relative to a detecting unit”as used herein encompasses cases where only the radiation source ismoved, only the detecting unit is moved, and both the radiation sourceand the detecting unit are moved.

It should be noted that each of the projection images and thetomographic image of the slice plane is formed by a plurality of pixelswhich are two-dimensionally and discretely arranged at a given samplinginterval, where the pixels are located at grid points corresponding tothe given sampling interval. The “pixel positions” as used herein refersto positions corresponding to the grid points on which pixel valuesforming an image are located on the projection image or the tomographicimage. On the other hand, the “coordinate positions” as used hereinincludes the grid points on which pixels forming a image are located,i.e., the pixel positions, and positions between the grid points, i.e.,positions where pixel values forming the image are not located. That is,the coordinate positions include not only the pixel positions but alsopositions between the pixel positions.

The projection images to be projected may be all the projection imagesobtained or two or more projection images of the projection imagesobtained.

The “desired slice plane” as used herein refers to a slice plane of thesubject for which the tomographic image is generated.

The description “while preserving the pixel values of the projectionimages” as used herein refers to that the pixel values of the projectionimages are not changed. It should be noted that, in the disclosure, thepixel value at a pixel position of the projection image may not be ableto be projected on a coordinate position on the slice plane. That is,depending on the positional relationship between the radiation sourceposition and the detecting unit, the pixel value of the projection imagecorresponding to the coordinate positions on the slice plane may not beat a pixel position of the projection image, but at a coordinateposition between pixel positions. In such a case, the pixel value at thecoordinate position on the projection image to be projected on thecoordinate position on the slice plane can be calculated byinterpolation using pixel values at pixel positions around thecoordinate position, for example. In this case, the pixel valuecalculated by interpolation is also a pixel value of the projectionimage, and the pixel value of the projection image calculated byinterpolation is projected on the corresponding coordinate position onthe slice plane while being preserved.

The “coordinate position of interest on the slice plane” as used hereinrefers to a coordinate position for which the pixel value is calculatedto generate the tomographic image of the slice plane. The tomographicimage of the slice plane can be generated by calculating the pixel valueat the coordinate position of interest with sequentially changing thecoordinate position of interest on the slice plane.

The “predetermined range relative to the coordinate position ofinterest” as used herein refers to a range of a predetermined number ofcoordinate positions or pixel positions around and including the pixelposition of interest. For example, a range of 3×3 coordinate positionsor pixel positions with the pixel position of interest being the center,or a range of 5×5 coordinate positions or pixel positions with the pixelposition of interest being the center may be set as the predeterminedrange relative to the coordinate position of interest. It should benoted that the size of the predetermined range may be fixed or may bechanged arbitrarily according to input by the operator.

In the tomographic image generation device according to the disclosure,the pixel value projecting unit may project, for each of the differentradiation source positions, pixel values at coordinate positions on thecorresponding projection image intersecting with straight lines thatconnect the radiation source position and individual pixel positions onthe slice plane as pixel values at the pixel positions on the sliceplane on the straight lines.

In the tomographic image generation device according to the disclosure,the pixel value projecting unit may project, for each of the differentradiation source positions, pixel values at pixel positions on thecorresponding projection image on straight lines that connect theradiation source position and the individual pixel positions on theprojection image as pixel values at coordinate positions on the sliceplane intersecting with the straight lines.

In this case, a spacing between coordinate positions on the slice planemay be smaller than a spacing between pixel positions on the sliceplane.

In the tomographic image generation device according to the disclosure,the pixel value calculating unit may calculate the pixel value at thecoordinate position of interest by performing regression analysis onpixel values of the projection images projected on the slice plane.

The “regression analysis” is a statistical technique for analyzing amultivariate relationship. It is assumed here that observed valuesobserved at observation points include noise added to the true values.The regression analysis is a technique to solve an inverse problem tofind the true value at every observation point by regression using aleast squares method, a moving average method, a kernel function, etc.In the disclosure, the pixel value at the coordinate position ofinterest is calculated with assuming that each coordinate position onthe slice plane with the pixel values of the projection images projectedthereon is the observation point, each pixel value at the observationpoint is the observed value, and a pixel value at the coordinateposition of interest is the true value.

In the tomographic image generation device according to the disclosure,the pixel value calculating unit may calculate pixel values at pixelpositions on the slice plane by performing the regression analysis togenerate a regression surface that represents a tomographic image of theslice plane, and sampling the regression surface at a desired samplinginterval, to thereby generate the tomographic image.

In this case, the sampling interval may be different from a samplinginterval of the projection images.

By changing the sampling interval of the regression surface, theresolution of the tomographic image can be changed. For example, asmaller sampling interval results in a higher resolution of thetomographic image. The “desired sampling interval” as used herein refersto a spacing between pixels with which the tomographic image having anecessary resolution is obtained. It should be noted that the desiredsampling interval may be fixed or may be changed arbitrarily accordingto input by the operator.

The description “different from a sampling interval of the projectionimages” as used herein encompasses both the cases where the samplinginterval of the regression surface is greater than the sampling intervalof the projection images, and where the sampling interval of theregression surface is smaller than the sampling interval of theprojection images. If the sampling interval of the regression surface isgreater than the sampling interval of the projection images, theresolution of the tomographic image is lower than the resolution of theprojection images. In contrast, if the sampling interval of theregression surface is smaller than the sampling interval of theprojection images, the resolution of the tomographic image is higherthan the resolution of the projection images.

In the tomographic image generation device according to the disclosure,if an instruction to change the size of an area of interest in thetomographic image being displayed is received, the pixel valuecalculating unit may generate a tomographic image of the area ofinterest with changing the sampling interval of an area of theregression surface corresponding to the area of interest according tothe instruction to change.

In the tomographic image generation device according to the disclosure,the pixel value calculating unit may change sharpness of the pixel valueat the coordinate position of interest when the regression analysis isperformed.

The description “change sharpness” as used herein encompassesemphasizing the sharpness such that an edge included in the generatedtomographic image is emphasized, and reducing the sharpness such thatthe generated tomographic image is smoothed to reduce noise.

In this case, the pixel value calculating unit may change a level ofchange of the sharpness depending on information of at least one ofimaging conditions under which the projection images are taken and astructure of the subject included in the projection images.

When the projection images are taken, a smaller amount of radiation thatreaches the detector results in more noise in the projection images. Theamount of noise in the projection images and the sharpness of theobtained images also vary depending on the radiation quality of thex-ray, i.e., whether the x-ray is a high voltage x-ray or a low voltagex-ray, the type of material forming the detecting unit, and/or thepresence or absence of a grid used to remove scattered rays duringimaging. The “imaging conditions” as used herein refer to variousconditions that influence the amount of noise and the sharpness of theprojection images, and examples thereof may include the amount ofradiation that reaches the detector during imaging, the type of thedetecting unit, and/or the presence or absence of the grid. The“structure of the subject” as used herein refers to a structure, such asan edge, included in the subject.

A preferred sharpness of the tomographic image depends on the preferenceof the user, such as a doctor, who observes the image. Therefore thesharpness may be changeable according to the preference of the user.

In the tomographic image generation device according to the disclosure,the pixel value calculating unit may calculate the pixel value at thecoordinate position of interest with removing an outlier pixel valueamong the pixel values of the projection images projected in thepredetermined range relative to the coordinate position of interest orweighting the outlier pixel value with a small weight.

The “outlier” as used herein refers to a pixel value that is largelydifferent from the other pixel values among the pixel values of theprojection images projected in the predetermined range relative to thecoordinate position of interest. The expression “largely different” asused herein means that a difference between the value of the outlier andan average value of the pixel values projected in the predeterminedrange relative to the coordinate position of interest, for example,exceeds a predetermined threshold value.

In the tomographic image generation device according to the disclosure,the pixel value projecting unit may correct, based on a positionalrelationship between a certain radiation source position and eachcoordinate position of interest on the projection image corresponding tothe certain radiation source position, a coordinate position on theslice plane on which a pixel value at the coordinate position ofinterest on the projection image is projected such that two-dimensionalcoordinates of the coordinate position of interest on the projectionimage corresponding to the certain radiation source position agrees withtwo-dimensional coordinates of the coordinate position on the sliceplane on which the pixel value at the coordinate position of interest onthe projection image is projected, and may project the pixel values ofthe projection images on the corrected coordinate positions on the sliceplane.

In this case, the image obtaining unit may obtain a radiographic imageof the subject taken by applying the radiation to the subject from thecertain radiation source position, the pixel value calculating unit maygenerate the tomographic image by calculating the pixel value at thecoordinate position of interest on the slice plane with the pixel valuesof the projection images being projected on the corrected coordinatepositions, and the tomographic image generation device may furthercomprise a display unit for displaying the radiographic image and thetomographic image.

The “radiographic image of the subject” as used herein refers to animage including a transmission image of a structure included in thesubject, which image being obtained by imaging the subject under imagingconditions for obtaining a transmission image of the subject with theradiation source position being fixed at the certain radiation sourceposition.

In the tomographic image generation device according to the disclosure,the pixel value projecting unit and the pixel value calculating unit maygenerate the tomographic image for each of a plurality of slice planesof the subject, and the tomographic image generation device may furthercomprise a pseudo image generating unit for generating a pseudo imagefrom the tomographic images.

The “pseudo image” as used herein refers to a pseudo image that appearsas an image of a type different from the tomographic image. An examplethereof is an addition tomographic image that is generated by simplyadding up pixel values at corresponding pixel positions of thetomographic images so that it appears as a transmission image obtainedby ordinary radiographic imaging. Besides the addition tomographicimage, a maximum projection image that appears as a three-dimensionalimage obtained by an MIP (Maximum Intensity Projection) method thatextracts maximum values from corresponding pixel positions of thetomographic images, and a minimum projection image that appears as athree-dimensional image obtained by a minIP (Minimum IntensityProjection) method that extracts minimum values from corresponding pixelpositions of the tomographic images can be used as the pseudo image.

In the tomographic image generation device according to the disclosure,the pixel value calculating unit may calculate weighting factors basedon a difference between the pixel value at the coordinate position ofinterest and the pixel value at the coordinate position of eachprojection image corresponding to the coordinate position of interest,and may calculate the pixel value at the coordinate position of interestagain based on the plurality of pixel values of the projection imagesand the weighting factors to calculate a new pixel value at thecoordinate position of interest.

In this case, the pixel value calculating unit may iterate calculatingnew weighting factors using the new pixel value at the coordinateposition of interest, and calculating a new pixel value at thecoordinate position of interest again based on the plurality of pixelvalues of the projection images and the new weighting factors.

As the “weighting factor”, for example, a smaller value may be used fora larger difference between the pixel value at the coordinate positionof interest and each pixel value at the coordinate position of eachprojection image corresponding to the coordinate position of interest.

The number of iterations of the process of calculating new weightingfactors using the new pixel value at the coordinate position ofinterest, and calculating a new pixel value at the coordinate positionof interest again based on the plurality of pixel values of theprojection images and the new weighting factors may be set in advance,or the process may be iterated until a given convergence condition, suchthat a difference between the new pixel value at the coordinate positionof interest and each pixel value at the coordinate position of eachprojection image corresponding to the coordinate position of interest isnot greater than a predetermined threshold value, is satisfied.

An aspect of a tomographic image generation method according to thedisclosure comprises the steps of:

obtaining a plurality of projection images corresponding to differentradiation source positions, the projection images being taken by movinga radiation source relative to a detecting unit and applying radiationto a subject from the different radiation source positions to which theradiation source is moved;

projecting pixel values of the projection images on coordinate positionson a desired slice plane of the subject based on a positionalrelationship between the radiation source position with which each ofthe projection images is taken and the detecting unit, while preservingthe pixel values of the projection images; and

calculating a pixel value at each coordinate position of interest on theslice plane based on a plurality of pixel values of the projectionimages projected in a predetermined range relative to the coordinateposition of interest on the slice plane to thereby generate atomographic image of the slice plane.

The tomographic image generation method according to the disclosure maybe provided in the form of a program for causing a computer to executethe tomographic image generation method.

According to the present disclosure, pixel values of the projectionimages are projected on coordinate positions on a desired slice plane ofthe subject based on the positional relationship between the radiationsource position with which each of the projection images is taken andthe detecting unit, while preserving the pixel values of the projectionimages. Then, the pixel value at each coordinate position of interest iscalculated based on a plurality of pixel values of the projection imagesprojected in a predetermined range relative to the coordinate positionof interest on the slice plane to generate a tomographic image. Whencompared with the conventional techniques where only the pixel values ofthe projection images projected on the coordinate position of interestare used to calculate the pixel value at the coordinate position ofinterest, the disclosure allows taking influence of pixel values aroundthe coordinate position of interest into account, thereby reducingartifacts to allow generation of a tomographic image with even higherimage quality. Further, since it is not necessary to repeat projectingthe pixel values again and again, which is necessary in the iterativeapproximation reconstruction method, significant reduction of thecalculation time can be achieved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating the schematic configuration of aradiographic imaging apparatus to which a tomographic image generationdevice according to a first embodiment of the disclosure is applied,

FIG. 2 is a diagram illustrating the radiographic imaging apparatusviewed from the direction of arrow A in FIG. 1,

FIG. 3 is a diagram illustrating the schematic configuration of thetomographic image generation device of the first embodiment implementedby installing a tomographic image generation program on a computer,

FIG. 4 is a diagram for explaining how projection images are obtained,

FIG. 5 is a diagram for explaining how pixel values are projected in thefirst embodiment,

FIG. 6 is a diagram for explaining how a pixel value of a projectionimage is interpolated,

FIG. 7 shows pixel values projected on a slice plane in the firstembodiment,

FIG. 8 is a diagram for explaining how a regression curve (regressionsurface) including outliers is generated,

FIG. 9 is a diagram for explaining how a regression curve (regressionsurface) from which outliers are removed is generated,

FIG. 10 is a flow chart illustrating a process performed in the firstembodiment,

FIG. 11 is a diagram for explaining how pixel values are projected in asecond embodiment,

FIG. 12 is a diagram showing pixel values projected on a slice plane inthe second embodiment,

FIG. 13 is a diagram showing a positional relationship between theposition of a structure on a slice plane and the position of thestructure projected on a radiation detector,

FIG. 14 is a diagram showing a difference between the position of astructure on a tomographic image and the position of the structure on aradiographic image,

FIG. 15 is a diagram illustrating the schematic configuration of atomographic image generation device of a fourth embodiment implementedby installing a tomographic image generation program on a computer,

FIG. 16 shows a state where an enlarged image of an area of interest isdisplayed on a display unit,

FIG. 17 is a diagram illustrating the schematic configuration of atomographic image generation device of a fifth embodiment implemented byinstalling a tomographic image generation program on a computer,

FIG. 18 shows a plurality of slice plane projection images withoutpositional misalignment,

FIG. 19 shows a plurality of slice plane projection images withpositional misalignment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, embodiments of the present disclosure will be describedwith reference to the drawings. FIG. 1 is a diagram illustrating theschematic configuration of a radiographic imaging apparatus to which atomographic image generation device according to a first embodiment ofthe disclosure is applied, and FIG. 2 is a diagram illustrating theradiographic imaging apparatus viewed from the direction of arrow A inFIG. 1. The radiographic imaging apparatus 1 is a mammographic apparatusthat images a breast M (which may hereinafter also be referred to as“subject M”) with different radiation source positions, which correspondto different imaging directions, and obtains a plurality of radiographicimages, i.e., projection images, to generate a tomographic image of thebreast by performing tomosynthesis imaging. As shown in FIG. 1, theradiographic imaging apparatus 1 includes an imaging unit 10, a computer2 connected to the imaging unit 10, and a display unit 3 and an inputunit 4 connected to the computer 2.

The imaging unit 10 includes an arm 12, which is coupled to a base (notshown) via a rotatable shaft 11. An imaging table 13 is attached to oneend of the arm 12, and a radiation applying unit 14 is attached to theother end of the arm 12 so as to face the imaging table 13. The arm 12is configured such that only the end to which the radiation applyingunit 14 is attached can be rotated, this allows only the radiationapplying unit 14 to be rotated while the imaging table 13 is fixed.Rotation of the arm 12 is controlled by the computer 2.

The imaging table 13 includes therein a radiation detector 15 (detectingunit), such as a flat panel detector. The imaging table 13 also includestherein a circuit board, etc., which includes a charge amplifier forconverting an electric charge signal read out from the radiationdetector 15 into a voltage signal, a correlated double sampling circuitfor sampling the voltage signal outputted from the charge amplifier, anAD converter for converting the voltage signal into a digital signal,etc.

The radiation detector 15 is of a type that is repeatedly usable torecord and read out a radiographic image on and from it. The radiationdetector 15 may be a so-called direct-type radiation detector, whichdirectly receives the radiation and generates electric charges, or maybe a so-called indirect-type radiation detector, which once converts theradiation into visible light, and then converts the visible light intoelectric charge signals. As the reading system to read out theradiographic image signal, it is desirable to use a so-called TFTreading system, which reads out the radiographic image signal withturning on and off TFT (thin film transistor) switches, or a so-calledoptical reading system, which reads out the radiographic image signal byapplying reading light. However, this is not intended to limit theinvention and any other type of radiation detector may be used.

The radiation applying unit 14 contains therein a x-ray source 16(radiation source). Timing of application of radiation from the x-raysource 16 and x-ray generation conditions (such as tube current, time,tube current time product, etc.) of the x-ray source 16 are controlledby the computer 2.

To the arm 12, a compression paddle 17 disposed above the imaging table13 for compressing the breast M, a support 18 for supporting thecompression paddle 17, and a moving mechanism 19 for moving the support18 in the vertical direction as in FIGS. 1 and 2 are attached.

The display unit 3 is a display device, such as a CRT or a liquidcrystal monitor. The display unit 3 displays projection images which areobtained as described later, a generated tomographic image, and messagesnecessary for operation, etc. The display unit 3 may include a built-inspeaker for outputting sound.

The input unit 4 is formed by a keyboard, a mouse, and/or a touch-panelinput device. The input unit 4 receives operation by the operator of theradiographic imaging apparatus 1. The input unit 4 also receives inputof various information, such as imaging conditions, necessary forperforming tomosynthesis imaging, and instructions to modify theinformation. In this embodiment, the individual units of theradiographic imaging apparatus 1 operate according to the informationinputted by the operator via the input unit 4.

A tomographic image generation program is installed on the computer 2.In this embodiment, the computer may be a work station or a personalcomputer which is directly operated by the operator, or may be a servercomputer connected to the work station or the personal computer via anetwork. The tomographic image generation program is distributed withbeing recorded on a recording medium, such as a DVD or a CD-ROM, and isinstalled on the computer from the recording medium. Alternatively, thetomographic image generation program is stored in a storage device of aserver computer connected to a network or a network storage such that itis externally accessible, and is downloaded and installed on thecomputer as necessary.

FIG. 3 is a diagram illustrating the schematic configuration of thetomographic image generation device implemented by installing thetomographic image generation program on the computer 2. As shown in FIG.3, the tomographic image generation device includes a CPU 21, a memory22, and a storage 23, as the configuration of a standard computer.

The storage 23 is formed by a storage device, such as a hard disk orSSD. The storage 23 stores various information including programs fordriving the individual units of the radiographic imaging apparatus 1,and the tomographic image generation program. The storage 23 also storesprojection images obtained by tomosynthesis imaging, and a tomographicimage which is generated as described later.

The memory 22 temporarily stores the programs stored in the storage 23for the CPU 21 to execute various operations. The tomographic imagegeneration program defines, as the operations to be executed by the CPU21: an image obtaining operation for causing the radiographic imagingapparatus 1 to perform tomosynthesis imaging to obtain a plurality ofprojection images of the breast M; a pixel value projecting operationfor projecting pixel values of the projection images on coordinatepositions on a desired slice plane of the breast M, which is thesubject, based on the positional relationship between the position ofthe x-ray source 16 with which each projection image is taken and theradiation detector 15, while preserving the pixel values of theprojection images; and a pixel value calculating operation forcalculating a pixel value of each coordinate position of interest basedon the pixel values of the projection images projected in apredetermined range relative to the coordinate position of interest onthe desired slice plane to generate a tomographic image.

When the CPU 21 executes the above-described operations according to thetomographic image generation program, the computer 2 functions as animage obtaining unit 31, a pixel value projecting unit 32, and a pixelvalue calculating unit 33. It should be noted that the computer 2 mayinclude CPUs for executing the image obtaining operation, the pixelvalue projecting operation, and the pixel value calculating operation,respectively.

The image obtaining unit 31 causes the arm 12 to rotate about therotatable shaft 11 to move the x-ray source 16, applies an x-ray to thebreast M, which is the subject, from different radiation sourcepositions to which the x-ray source 16 is moved, and detects the x-raytransmitted through the breast M with the radiation detector 15 toobtain a plurality of projection images Gi (i=1 to n, where n is thenumber of radiation source positions) corresponding to the differentradiation source positions. FIG. 4 is a diagram for explaining how theprojection images Gi are obtained. As shown in FIG. 4, the x-ray source16 is moved to each of radiation source positions S1, S2, . . . , Sn,and the x-ray source 16 is activated at each radiation source positionto apply an x-ray to the breast M. Then, the x-ray transmitted throughthe breast M is detected with the radiation detector 15 to obtainprojection images G1, G2, . . . , Gn corresponding to the radiationsource positions S1 to Sn. The obtained projection images Gi are storedin the storage 23. It should be noted that the projection images Gi maybe obtained and stored in the storage 23 according to a program separatefrom the tomographic image generation program. In this case, the imageobtaining unit 31 reads out the projection images Gi, which are storedin the storage 23, from the storage 23 for the pixel value projectingoperation and the pixel value calculating operation.

In this embodiment, all the projection images Gi stored in the storage23 may be read out to be used for the pixel value projecting operationand the pixel value calculating operation, or a predetermined number of(two or more) projection images Gi among the projection images Gi storedin the storage 23 may be read out to be used for the pixel valueprojecting operation and the pixel value calculating operation.

The pixel value projecting unit 32 projects pixel values of theprojection images obtained by the image obtaining unit 31 on coordinatepositions on a desired slice plane of the breast M while preserving thepixel values of the projection images. FIG. 5 is a diagram forexplaining how the pixel values are projected in the first embodiment.It should be noted that FIG. 5 explains a case where a projection imageGi obtained with a radiation source position Si is projected on adesired slice plane Tj (j=1 to m, where m is the number of slice planes)of the breast M.

Each of the projection image Gi and the tomographic image of the sliceplane Tj, which is generated as described later, is formed by aplurality of pixels which are two-dimensionally and discretely arrangedat a given sampling interval, where the pixels are located at gridpoints corresponding to the given sampling interval. In FIG. 5 and FIG.11, which will be described later, the short line segments orthogonallycrossing the projection image Gi and the slice plane Tj representboundary positions between the pixels. In FIG. 5 and FIG. 11, which willbe described later, each center position between the pixel boundarypositions is a pixel position, which is the grid point. As shown in FIG.5, in the first embodiment, pixel values at positions on the projectionimage Gi intersecting with the straight lines that connect the radiationsource position Si and the individual pixel positions on the slice planeTj are projected as pixel values at the pixel positions on the sliceplane Tj on the corresponding straight lines.

Assuming that coordinates of the radiation source position Si are (sxi,syi, szi), and coordinates of a pixel position on the slice plane Tj areTj(tx, ty, tz), coordinates (pxi, pyi) of the corresponding coordinateposition Pi on the projection image Gi are expressed by the equations(1) below. In this embodiment, the z-axis is set in the directionperpendicular to the detection surface of the radiation detector 15, they-axis is set in the direction parallel to the direction in which theposition of the x-ray source 16 on the detection surface of theradiation detector 15 is moved, and the x-axis is set in the directionorthogonal to the y-axis.

pxi=(tx×szi−sxi×tz)/(szi−tz),

pyi=(ty×szi−syi×tz)/(szi−tz)  (1).

It should be noted that the coordinate position Pi on the projectionimage Gi may not be a pixel position on the projection image Gi. Forexample, as shown in FIG. 6, a coordinate position Pi on the projectionimage Gi may be between four pixel positions O1 to O4 on the projectionimage Gi. In this case, interpolation calculation is performed usingpixel values at the four pixel positions O1 to O4, which are nearest tothe coordinate position Pi of the projection image Gi, as shown in FIG.6, to calculate the pixel value at the coordinate position Pi, and thecalculated pixel value is projected on the pixel position Tj(tx, ty, tz)on the slice plane Tj. As the interpolation calculation, any technique,such as linear interpolation calculation where the pixel values at thefour pixel positions are weighted depending on the distance between thecoordinate position Pi and each of the four pixel positions, non-linearbicubic interpolation calculation using pixel values at more pixelpositions around the coordinate position Pi, or B-spline interpolationcalculation, may be used. In place of performing the interpolationcalculation, the pixel value at the pixel position which is nearest tothe coordinate position Pi may be used as the pixel value at thecoordinate position Pi.

The pixel value projecting unit 32 projects, for each radiation sourceposition Si, the pixel values of the corresponding projection image Gion the slice plane Tj. As a result, n pixel values corresponding to thenumber of projection images are projected on each pixel position on theslice plane Tj, as shown in FIG. 7. FIG. 7 shows a state where pixelvalues of five projection images are projected on each pixel position.In FIG. 7, and in FIGS. 8, 9, 12, 18, and 19, which will be describedlater, the short line segments orthogonally crossing the slice plane Tjrepresent boundary positions between pixels, and the center positionsbetween the pixel boundary positions are the pixel positions, which arethe grid points.

The pixel value calculating unit 33 generates a tomographic image of theslice plane Tj by calculating each pixel value on the slice plane Tj.Specifically, the pixel value at each coordinate position of interest iscalculated based on a plurality of pixel values of the projection imagesprojected in a predetermined range relative to the coordinate positionof interest for which the pixel value is calculated. The coordinateposition of interest may be a pixel position on the slice plane Tj.While the pixel values of the projection images Gi are projected on thepixel positions on the slice plane Tj in the first embodiment, the pixelvalue at each coordinate position of interest may be calculated usingthe pixel values projected on the coordinate position of interest, orwithout using the pixel values projected on the coordinate position ofinterest. Now, how the pixel value at each coordinate position ofinterest is calculated is described.

The pixel values of the projection images Gi projected on the sliceplane Tj by the pixel value projecting unit 32 tend to be more similarwhen they are nearer to each other. Therefore the pixel valuecalculating unit 33 performs an operation to change the sharpness suchthat the pixel values projected on the slice plane Tj are smoothlycontinuous. In this embodiment, the pixel values projected on the sliceplane Tj are filtered with a smoothing filter. Specifically, pixelvalues at pixel positions in a predetermined range, such as 3×3 or 5×5,with the coordinate position of interest being the center are filteredwith a Gaussian filter, for example. With this, the pixel values ofpixels at and around the coordinate position of interest become smoothlycontinuous, thereby suppressing noise, such as quantum noise, which isoriginally included in the projection images Gi, in the pixel valuesprojected on the slice plane Tj.

A value defining the size of the predetermined range may be stored as afixed value in the storage 23. Further, the value may be changedarbitrarily according to input by the operator via the input unit 4. Inthis case, the value defining the size of the predetermined range storedin the storage 23 is rewritten according to input by the operator viathe input unit 4 and the size of the predetermined range is changed.

The level of smoothness, i.e., the level of noise suppression can bechanged by changing the filter size of the Gaussian filter.Specifically, increasing the filter size to increase the range offiltering with the coordinate position of interest being the centerallows higher level of noise suppression. It should be noted that alower amount of x-ray reaching the radiation detector 15 when theprojection images Gi are taken results in more noise in the projectionimages Gi, which in turn results in more noise in the pixel valuesprojected on the slice plane Tj. The amount of noise in the projectionimages Gi also varies depending on the radiation quality of the x-ray,i.e., whether the x-ray is a high voltage x-ray or a low voltage x-ray.The amount of noise in the projection images Gi also varies depending onthe type of the radiation detector 15 used to take the projectionimages. Further, in some cases, a scattered ray removing grid may bedisposed between the radiation detector 15 and the subject M when theprojection images Gi are taken in order to prevent influence ofscattered ray of the x-ray on the subject M. The amount of noise in theprojection images Gi also varies depending on the type of the scatteredray removing grid, or the presence or absence of the scattered rayremoving grid.

For this reason, in this embodiment, properties of the smoothing filterare changed based on the imaging conditions, such as the amount of x-rayreaching the radiation detector 15, the radiation quality of the x-ray,the type of the radiation detector 15, the type of the scattered rayremoving grid, and the presence or absence of the scattered ray removinggrid. For example, for the imaging conditions which result in more noisein the projection images Gi, the filter size is increased so that higherlevel of noise suppression is achieved.

When a Gaussian filter is used for the filtering, edges which arestructures of the subject M included in the tomographic image, which isgenerated as described later, may be blurred. For this reason, thefiltering may be performed using a bilateral filter which weightsneighboring pixels around the coordinate position of interest dependingon the distance between the pixels, and also weights the neighboringpixels around the coordinate position of interest with normallydistributed weights such that the weight is smaller when the differencebetween pixel values is greater. Alternatively, the filtering may beachieved using a non-local means filter which performs weighting basedon similarity between a neighboring area around the coordinate positionof interest on the slice plane Tj and a neighboring area around anarbitrary pixel on the slice plane Tj. This allows suppressing noisewhile preserving edges, thereby preventing lowering of the sharpness ofthe tomographic image which is generated as described later.

Further, the pixel values projected on the slice plane Tj may befiltered with a differential filter, for example, to detect an edgewhich is the structure of the subject, where there is a sudden change inthe pixel value exceeding a predetermined threshold value, and thefilter properties may be changed such that the filtering is appliedalong the direction in which the edge extends, to thereby change thelevel of change of the sharpness. Still further, the filtering may beperformed such that, with respect to pixel values along a boundary of anedge, pixel values at positions beyond the edge are not used. Thisallows preventing the edge from being smoothed, thereby preventinglowering of the sharpness of the distribution of the pixel valuesprojected on the slice plane Tj while suppressing noise.

In place of or in addition to the smoothing, an operation to emphasizethe sharpness may be performed to emphasize edges. In this case, it ispreferred to perform the operation to emphasize the sharpness along thedirection in which each edge extends.

After the filtering is performed as described above, the pixel valuecalculating unit 33 performs regression analysis on the pixel values ofthe projection images projected on the slice plane Tj to generate acurved surface, or a regression surface, that represents a tomographicimage of the slice plane Tj. In the following description, theregression surface is considered as a regression curve for ease ofexplanation. The regression analysis is a statistical technique foranalyzing a multivariate relationship. It is assumed here that observedvalues observed at observation points include noise added to the truevalues. The regression analysis is a technique to solve an inverseproblem to find the true value at every observation point by regressionusing a least squares method, a moving average method, a kernelfunction, etc. In the first embodiment, a pixel value rm at eachcoordinate position of interest um is calculated by the regressionanalysis with assuming that each coordinate position on the slice planeTj with the pixel values of the projection images Gi projected thereonis an observation point uk, each pixel value of the projection imagesprojected on the observation point uk is an observed value qk, and thepixel value calculated for the coordinate position of interest um is atrue value rm.

In the case where a least squares method is used, it is assumed that thetrue value follows a function whose distribution is defined by γparameters a, i.e., r=f(u|a1, a2, . . . , aγ). Then, the function f canbe determined by finding the parameters a1, a2, . . . , aγ whichminimize squared errors between the true values and the observed values.Specifically, the pixel value rm at each coordinate position of interestis calculated by determining the parameters of the function f such thatthe total sum of errors of the observed values at the observation pointsis minimized, according to the equation (3) below, to generate theregression curve (regression surface). It should be noted that, as shownby the equation (4) below, a weight wk may be set for each observationpoint uk, and the regression curve (regression surface) may be generatedby calculating the pixel value rm at each coordinate position ofinterest um by the weighted least squares method.

$\begin{matrix}{r_{m} = {\sum\limits_{k}\left\{ {q_{k} - {f\left( u_{k} \right)}} \right\}^{2}}} & (3) \\{r_{m} = {\sum\limits_{k}{w_{k}\left\{ {q_{k} - {f\left( u_{k} \right)}} \right\}^{2}}}} & (4)\end{matrix}$

In the case where a moving average method is used, the regressionsurface is generated by calculating the pixel value at each coordinateposition of interest by the moving average method. Specifically,considering the regression surface as a regression curve for ease ofexplanation, for the pixel value at each coordinate position of interesturn, an average value {(qk−1)+qk+(qk+1)}/3 of the pixel values of theprojection images Gi projected on three coordinate positions adjacent tothe coordinate position of interest um, i.e., coordinate positions uk−1,uk, and uk+1, for example, is calculated, and the calculated averagevalue is used as the pixel value at the coordinate position of interesturn. It should be noted that a weight may be set for each pixel value.For example, weights may be set such that the weight is smaller as thedistance from the coordinate position of interest um is greater.

In the case where regression using a kernel function is used, theregression curve (regression surface) is calculated by determining akernel function, according to the equation (5) below, for eachcoordinate position of interest um and the observation point uk on theslice plane Tj on which the pixel values of the projection images areprojected. The “argmin” in the equation (5) means that the value ofr(um) that minimizes the right side is calculated.

$\begin{matrix}{{r\left( u_{m} \right)} = {\arg \; {\min\limits_{r{(u_{m\; i\; n})}}{\sum\limits_{k}{\left\{ {q_{k} - {r\left( u_{m} \right)}} \right\}^{2}{K\left( {u_{k},u_{m},q_{k},q_{m}} \right)}}}}}} & (5)\end{matrix}$

The above-described filtering for smoothing can be integrated into theregression analysis. In the case where the least squares method is used,using a low-dimensional function as the function f results in a higherlevel of smoothing of the generated regression surface. In contrast,using a high-dimensional function as the function f results in a higherlevel of sharpness of the generated regression surface. In the casewhere the moving average is used, the level of smoothing can be changedby changing the number of pixels for which the average is calculated, orchanging the level of weighting. Namely, increasing the number of pixelsfor which the average is calculated results in a higher level ofsmoothing. Also, the level of smoothing may be changed by changing thelevel of weighting depending on the imaging conditions, as describedabove.

With the regression technique using a kernel function, the level ofsmoothing can be changed depending on the design of the kernel function.In particular, the regression technique using a kernel function allowsobtaining an effect similar to that of the weighted least squares methodand emphasizing edges depending on the design of the kernel function.For example, when the kernel function expressed by the equation (6)below is used, the regression surface is generated such that a pixelvalue closer to the observed value qk at the observation point uk iscalculated when the distance between the coordinate position of interestum and the observation point uk is smaller. This allows obtaining asmoothing effect similar to that obtained by using a Gaussian filter.The “hx” in the equation (6) is a bandwidth parameter.

$\begin{matrix}{{K\left( {u_{k},u_{m}} \right)} = {\exp\left( \frac{- {{u_{k} - u_{m}}}^{2}}{h_{x}^{2}} \right)}} & (6)\end{matrix}$

In FIG. 7, two pixel values among the five pixel values projected on therightmost pixel position on the slice plane Tj are largely differentfrom the pixel values at the adjacent pixel positions. If there arepixel values that are largely different from the pixel values of theadjacent pixels, the value of the generated regression surface at thepixel position which includes the outliers is largely different from thevalue at the adjacent pixel position, as shown in FIG. 8. Then, when atomographic image is generated from the calculated regression surface,as described later, the tomographic image includes an artifact at thepixel position corresponding to the outliers.

For this reason, the pixel value calculating unit 33 determines a pixelvalue which is largely different from the adjacent pixel values amongthe pixel values projected on the slice plane Tj as an outlier, andcalculates the pixel value at each coordinate position of interest withremoving the outlier pixel value. For example, the pixel valuecalculating unit 33 calculates a difference between each of the pixelvalues projected on the coordinate position of interest and an averagevalue of pixel values at pixel positions adjacent to the coordinateposition of interest on the slice plane Tj, and determines a pixel valuewhose difference from the average value exceeds a predeterminedthreshold value as an outlier to remove the outlier pixel value when theregression analysis is performed. In place of removing the outlier, theoutlier pixel value may be weighted with a small weight.

When the regression curve (regression surface) is calculated withremoving the outliers or weighting the outliers with a small weight, thevalue at the pixel position including the outliers does not differlargely from the value at the adjacent pixel position, as shown in FIG.9. This allows preventing the tomographic image from including anartifact.

The operation to remove an outlier can be integrated into the regressionanalysis. In the case where the least squares method is used, theweighted least squares method shown by the equation (4) above may beused with weighting the outlier pixel values with 0 or a small weight.In the case where the moving average is used, a weighted average may becalculated with weighting the outlier pixel values with 0 or a smallweight.

After the regression surface is generated, the pixel value calculatingunit 33 samples the regression surface at a desired sampling interval togenerate a tomographic image. The sampling interval may be stored in thestorage 23 as a fixed value. The sampling interval may be changeable toan arbitrary value according to an instruction made via the input unit4. For example, if the same sampling interval as that of the projectionimages is set, the tomographic image has the same resolution as that ofthe projection images Gi. If the sampling interval is set smaller thanthat of the projection images Gl, the tomographic image has a higherresolution than that of the projection images Gi. In contrast, if thesampling interval is set greater than that of the projection images Gi,the tomographic image has a lower resolution than that of the projectionimages Gi. In this case, the value of the sampling interval stored inthe storage 23 is rewritten according to input by the operator via theinput unit 4 and the sampling interval is changed. Alternatively, thesampling interval may be adjusted depending on the resolution of thedisplay unit 3.

Next, a process performed in the first embodiment is described. FIG. 10is a flow chart showing the process performed in the first embodiment.In response to an instruction to start the process made by the operatorand received by the input unit 4, the tomosynthesis imaging isperformed, and the image obtaining unit 31 obtains a plurality ofprojection images Gi (step ST1). Then, the pixel value projecting unit32 projects pixel values of the projection images Gi on coordinatepositions on a desired slice plane Tj of the breast M, while preservingthe pixel values of the projection images obtained by the imageobtaining unit 31 (step ST2).

Subsequently, the pixel value calculating unit 33 performs theregression analysis on the pixel values of the projection images Giprojected on the slice plane Tj (step ST3) to generate a regressionsurface that represents a tomographic image of the slice plane Tj (stepST4). Further, the pixel value calculating unit 33 samples theregression surface at a given sampling interval to generate atomographic image (step ST5), and the process ends. It should be notedthat, when another tomographic image at a different slice plane is to begenerated, the operations in steps ST1 to ST5 are performed withchanging the position of the slice plane.

As described above, in the first embodiment, pixel values of each of theprojection images Gi are projected on coordinate positions on a desiredslice plane Tj of the breast M, which is the subject, based on thepositional relationship between the position of the x-ray source 16 withwhich each projection image Gi is taken and the radiation detector 15,while preserving the pixel values of the projection images Gi. Then, thepixel value at each coordinate position of interest is calculated bygenerating a regression surface by regression analysis, for example,based on the pixel values of the projection images Gi projected in apredetermined range on the slice plane Tj relative to the coordinateposition of interest, to generate a tomographic image. When comparedwith the conventional techniques where only the pixel values of theprojection images Gi projected on each coordinate position of interestare used to calculate the pixel value at the coordinate position ofinterest, this embodiment allows taking influence of pixel values aroundthe coordinate position of interest into account, thereby reducingartifacts to allow generation of a tomographic image with even higherimage quality. Further, since it is not necessary to repeat projectingthe pixel values again and again, which is necessary in the iterativeapproximation reconstruction method, significant reduction of thecalculation time can be achieved.

Further, a tomographic image with a desired resolution can be generatedby calculating the pixel value at each coordinate position of interestby sampling the regression surface at a desired sampling interval.

Next, a second embodiment of the disclosure is described. It should benoted that the configuration of the tomographic image generation deviceaccording to the second embodiment is the same as the above-describedconfiguration of the tomographic image generation device according tothe first embodiment, and only the process performed is different.Therefore detailed description of the device is omitted in the followingdescription. In the above-described first embodiment, pixel values ofeach of the projection images Gi at positions intersecting with thestraight lines that connect the radiation source position and theindividual pixel positions on the slice plane Tj, as shown in FIG. 5,are projected as pixel values at the pixel positions on the slice planeTj on the straight lines. Whereas, in the second embodiment, for each ofthe different radiation source positions Si, pixel values at pixelpositions on the corresponding projection image Gi on straight linesthat connect the radiation source position Si and the individual pixelpositions on the projection image Gi are projected on coordinatepositions on the slice plane Tj intersecting with the straight lines.

FIG. 11 is a diagram for explaining how the pixel values are projectedin the second embodiment. It should be noted that FIG. 11 explains acase where a projection image Gi obtained at a radiation source positionSi is projected on a desired slice plane Tj (j=1 to m, where m is thenumber of slice planes) among slice planes of the breast M. As shown inFIG. 11, in the second embodiment, pixel values at pixel positions ofthe projection image Gi on the straight lines that connect the radiationsource position Si and the individual pixel positions on the projectionimage Gi are projected as pixel values at coordinate positions on theslice plane Tj intersecting with the straight lines. The relationshipamong the coordinates (sxi, syi, szi) of the radiation source positionat the radiation source position Si, the coordinates Tj(tx, ty, tz) of apixel position on the slice plane Tj, and the coordinates (pxi, pyi) ofa coordinate position Pi on the projection image Gi are as shown by theequations (1) above. Therefore the coordinate position on the sliceplane Tj on which the pixel value at each pixel position on theprojection image Gi is projected can be calculated by solving theequations (1) for tx and ty, where pxi and pyi in the equations (1) arethe pixel position on the projection image Gi. In this manner, eachpixel value of each projection image Gi is projected on the calculatedcoordinate position on the slice plane Tj.

In this case, as shown in FIG. 11, intersection points Tjx between theslice plane Tj and the straight lines that connect the radiation sourceposition Si and the individual pixel positions on the projection imageGi may not be pixel positions on the slice plane Tj. In this case, inthe second embodiment, the pixel values of the projection image Gi areprojected on coordinate positions between the pixel positions on theslice plane Tj. This means that, in the second embodiment, the pixelvalues of the projection image are projected also on coordinatepositions other than the pixel positions on the slice plane Tj.

In the second embodiment, the pixel value projecting unit 32 projects,for all the radiation source positions Si, the pixel values of all theprojection images G1 to Gn on the slice plane Tj. Thus, pixel valuescorresponding to the number of pixels of all the projection images Giare projected on coordinate positions including the pixel positions onthe slice plane Tj, as shown in FIG. 12.

Similarly to the first embodiment, the pixel value calculating unit 33in the second embodiment performs the filtering on the pixel values ofthe projection images Gi projected on the slice plane Tj, and performsthe regression analysis to generate a regression surface. The filteringis performed with setting each coordinate position on the slice plane onwhich the pixel values are projected as the center.

In the second embodiment, since the pixel values of the projectionimages Gi are projected on coordinate positions on the slice plane Tj,as described above, it is not necessary to perform interpolation of thepixel values of the projection images Gi, which is necessary in thefirst embodiment. Compared with the first embodiment, image quality ofthe projection images is not degraded when they are projected. Thisallows achieving even higher image quality of the generated tomographicimage.

Further, in the second embodiment, a spacing between the coordinatepositions on the slice plane Tj on which the pixel value are projectedis smaller than a spacing between the pixel positions on the slice planeTj, and coordinate positions other than the pixel positions on the sliceplane Tj also have pixel values. This allows generating a highlyaccurate regression surface based on the actually obtained pixel valuesof the projection images, even in a frequency band higher than theNyquist frequency, which is determined by the spacing between the pixelpositions on the slice plane Tj. Therefore, in the second embodiment,degradation of image quality can be suppressed even when a smallsampling interval of the regression surface is set, thereby allowinggeneration of a tomographic image with even higher image quality.

Next, a third embodiment of the disclosure is described. It should benoted that the configuration of the tomographic image generation deviceaccording to the third embodiment is the same as the above-describedconfiguration of the tomographic image generation device according tothe first embodiment, and only the process performed is different.Therefore detailed description of the device is omitted in the followingdescription. The difference between the third embodiment and the firstembodiment lies in that, in the third embodiment, the image obtainingunit 31 further obtains a radiographic image by ordinary x-ray imaging,and the pixel value projecting unit 32 corrects projection positions ona slice plane Tj on which pixel values of the projection images areprojected. It should be noted that the “ordinary x-ray imaging” as usedherein refers to x-ray imaging where the x-ray source 16 is not movedand is fixed at a certain radiation source position, and the x-ray isapplied to the subject under imaging conditions for obtaining atransmission image of the subject.

As shown in FIG. 13, the x-ray emitted from the x-ray source 16 is acone beam, which spreads as it travels away from the x-ray source 16.The position of the surface of the radiation detector 15, at which theprojection images Gi are obtained, is farther from the x-ray source 16than the slice plane Tj. Therefore when the breast M is imaged with acertain radiation source position among different radiation sourcepositions Si, the position of a structure BO, such as a mammary glandand a calcification, included in the breast M on the projection image Gidetected by the radiation detector 15 is different from the position ofthe structure BO in a tomographic image TGj of the slice plane Tj, asshown in FIG. 14.

When a radiographic image is obtained by the ordinary x-ray imaging, theposition of the x-ray source 16 is fixed at a certain radiation sourceposition, and the breast M is imaged under imaging conditions forobtaining a transmission image of the breast M. Therefore thegeometrical positional relationship of the projection image obtainedwith the certain radiation source position is the same as that of theradiographic image. In this case, when the obtained radiographic imageand the tomographic image are displayed side by side for diagnosis, theposition of the structure BO in the radiographic image differs from theposition of the structure 130 in the tomographic image. In the thirdembodiment, the pixel value projecting unit 32 corrects the coordinateposition on the slice plane Tj on which the pixel value at eachcoordinate position of interest on the projection image Gi is projectedbased on the positional relationship between the radiation sourceposition Si with which the projection image Gi is taken and thecoordinate position of interest on the projection image Gi, such thatthe coordinate position of interest on the projection image Gi agreeswith the coordinate position on the slice plane Tj on which the pixelvalue at the coordinate position of interest is projected.

Now, how the projection positions are corrected is described. As shownin FIG. 13, assuming that coordinates of the radiation source positionat the radiation source position Si are (sxi, syi, szi), and coordinatesof the structure BO on the slice plane Tj are Tj(tx, ty, tz),coordinates Pi(pxi, pyi) of the projection position on the radiationdetector 15 on which the structure BO is projected are expressed by theequations (1) above.

Assuming that Pi is the coordinate position of interest, if thecoordinate positions are not corrected, the coordinate position ofinterest Pi is projected on a coordinate position Tj on the slice planeTj, and the coordinate position on the slice plane Tj on which the pixelvalue at the coordinate position of interest Pi is projected can becalculated by solving the equations (1) for tx and ty.

On the other hand, as shown in FIG. 13, when the x-ray source 16 ispresent on a line which is orthogonal to the detection surface of theradiation detector 15 and crosses the coordinate position Pi(pxi, pyi),the coordinate position of interest Pi is projected at the intersectionpoint on the tomographic image of the slice plane Tj between the sliceplane Tj and the straight line that connects the radiation sourceposition Sc and the coordinate position Pi. In this case, the positionof the structure BO on the tomographic image of the slice plane Tj is atthe same two-dimensional coordinates as those on the projection image Gitaken with the radiation source position Sc, and the position of thestructure BO on the projection image Gi agrees with the position of thestructure BO on the tomographic image of the slice plane Tj. Thereforethe coordinate position on the slice plane Tj on which the pixel valueat the coordinate position of interest is projected is corrected bychanging the radiation source position which serves as the referencewhen the pixel value of the projection image is projected on the sliceplane Tj to the radiation source position Sc, which is present on thestraight line that is orthogonal to the coordinate position of the pixelvalue to be projected on the projection image. Assuming that thecoordinate position of the radiation source position Sc serving as thereference for the correction is (sxc, syc, szc), the relationshipbetween the coordinate position of interest Pi and the coordinateposition (tx,ty) on the slice plane Tj after the correction is expressedby the equation (7) below.

$\begin{matrix}{{P_{i}\left( {{px}_{i},{py}_{i}} \right)} = \left( {{{\frac{{sz}_{i}}{{sz}_{i} - {tz}}\frac{{sz}_{c} - {tz}}{{sz}_{c}}{tx}} - {\frac{tz}{{sz}_{i} - {tz}}{sx}_{i}} + {\frac{{sz}_{i}}{{sz}_{i} - {tz}}\frac{tz}{{sz}_{c}}{sx}_{c}}},{{\frac{{sz}_{i}}{{sz}_{i} - {tz}}\frac{{sz}_{c} - {tz}}{{sz}_{c}}{ty}} - {\frac{tz}{{sz}_{i} - {tz}}{sy}_{i}} + {\frac{{sz}_{i}}{{sz}_{i} - {tz}}\frac{tz}{{sz}_{c}}{sy}_{c}}}} \right)} & (7)\end{matrix}$

In the equation (7), (sz_(c)−tz)/sz_(c) in the first term of theequation expressing each of pxi and pyi represents the enlargementfactor at the coordinate position, and the third term represents theamount of shift of the coordinate position in the x direction or the ydirection. Therefore the corrected coordinate position on the sliceplane Tj on which the pixel value at the coordinate position of interestPi is projected can be calculated by solving the equation (7) for tx andty.

By correcting the coordinate positions on the slice plane Tj on whichthe pixel values of the projection images Gi are projected in thismanner, the position of a structure, such as a tumor, included in thetomographic image can be made the same as the position of thecorresponding structure included in the projection image, i.e., theradiographic image. This allows more accurate diagnosis using theradiographic image and the tomographic image.

Next, a fourth embodiment of the disclosure is described. FIG. 15 is adiagram illustrating the schematic configuration of a tomographic imagegeneration device according to the fourth embodiment. It should be notedthat the elements shown in FIG. 15 that are the same as those shown inFIG. 3 are denoted by the same reference numerals, and a detaileddescription thereof is omitted. The difference between the fourthembodiment and the first embodiment lies in that the tomographic imagegeneration device according to the fourth embodiment includes a pseudoimage generating unit 34 for generating a pseudo image from a pluralityof tomographic images of a plurality of slice planes of the breast M.

The pseudo image generating unit 34 generates as the pseudo image anaddition tomographic image by adding up corresponding pixel positions ofa plurality of tomographic images TGj generated for a plurality of sliceplanes Tj. The thus generated addition tomographic image shows a pseudotransmission image of the subject, which appears as the same as aradiographic image obtained by the ordinary x-ray imaging. In thisembodiment, the tomographic images have high image quality with reducednoise. By adding up such tomographic images, a high quality transmissionimage, i.e., a high quality pseudo radiographic image, can be generated.

In the fourth embodiment, when the pixel values of the projection imagesare projected on coordinate positions on each slice plane, thecoordinate positions on the slice plane Tj are corrected similarly tothe third embodiment to make the position of a corresponding structurethe same among the tomographic images. This facilitates determiningcorresponding pixel values to perform the addition, thereby allowinggeneration of a radiographic image with even higher image quality.

It should be noted that, in place of an addition tomographic image, thepseudo image generating unit 34 may generate as the pseudo image amaximum projection image which is obtained by an MIP method thatextracts maximum values from the corresponding pixel positions of theplurality of tomographic images. Alternatively, the pseudo imagegenerating unit 34 may generate as the pseudo image a minimum projectionimage which is obtained by a minIP method that extracts minimum valuesfrom the plurality of tomographic images.

When the generated tomographic image is displayed on the display unit 3in the above-described embodiments, an instruction to change the size ofan area of interest on the tomographic image may be received to displayan enlarged image of the area of interest for which the instruction tochange the size is received. In this case, an area of the regressionsurface corresponding to the area of interest for which the instructionto change the size has been received is extracted, and a samplinginterval which is smaller than the sampling interval of the tomographicimage is set to sample the extracted area. This allows displaying anenlarged image A2 of the area of interest A1 specified on thetomographic image TGj, as shown in FIG. 16. The sampling interval hereis preferably a sampling interval that is determined by the resolutionof the display unit 3. While the enlarged image A2 shown in FIG. 16 issuperimposed on the tomographic image TGj, the enlarged image A2 may bedisplayed in place of the tomographic image TGj, or the enlarged imageA2 may be displayed side by side with the tomographic image TGj. In acase where an instruction to reduce an area of interest is made, asampling interval that is greater than the sampling interval of thetomographic image is set to sample an extracted area of the regressionsurface corresponding to the area of interest.

Next, a fifth embodiment of the disclosure is described. FIG. 17 is adiagram illustrating the schematic configuration of a tomographic imagegeneration device according to the fifth embodiment. It should be notedthat the elements shown in FIG. 17 that are the same as those shown inFIG. 3 are denoted by the same reference numerals, and a detaileddescription thereof is omitted. The difference between the fifthembodiment and the first embodiment lies in that the tomographic imagegeneration device according to the fifth embodiment includes apositional misalignment correcting unit 35 for correcting for positionalmisalignment between a plurality of slice plane projection images TGi,each slice plane projection image TGi being defined as an image formedby pixel values of each of the projection images Gi projected on theslice plane Tj.

When the tomosynthesis imaging is performed, it is difficult toaccurately move the radiation source to the calculated radiation sourcepositions, due to influence of a mechanical error, such as vibrationduring imaging or mechanical misalignment, and the radiation sourcepositions during imaging may be different from the calculated radiationsource positions. This positional error, or positional misalignment,hinders accurate alignment of the projection position of an object,resulting in degradation of the image quality of the tomographic image.

Further, when such tomosynthesis imaging is performed, a plurality ofimages of the subject are taken based on an instruction to start animaging operation, and this imaging operation takes several seconds fromthe start to the end of the imaging operation, during which the subjectmay move. When there is such a body motion of the subject, it isdifficult to accurately align the projection position of the objectduring the reconstruction, resulting in degradation of the image qualityof the tomographic image.

Furthermore, the influence of a mechanical error and a body motionappears three-dimensionally and non-linearly in the subject, and it isdifficult to remove the influence of a mechanical error and a bodymotion from the tomographic image by simply translating, rotating, andenlarging or reducing the projection images Gi by affine transformation,etc.

In the fifth embodiment, the positional misalignment correcting unit 35corrects the positional misalignment between the slice plane projectionimages TGi. If there is no mechanical error and no body motion of thebreast M during the imaging operation with moving the x-ray source 16 todifferent radiation source positions Si, the pixel values of the sliceplane projection images TGi substantially agree with one another, asshown in FIG. 18. On the other hand, if there is a mechanical error or abody motion, a slice plane projection image corresponding to aprojection image that is taken when the mechanical error or the bodymotion occurs has pixel positions that are shifted from thecorresponding pixel positions of the other slice plane projectionimages, as shown in FIG. 19. The positional misalignment correcting unit35 corrects the positional misalignment between the slice planeprojection images TGi such that the positions of the slice planeprojection images TGi agree with one another. Specifically, thepositional misalignment correcting unit 35 detects feature points, suchas an edge, an intersection point between edges, an corner of an edge,etc., included in each slice plane projection image TGi by using analgorithm such as SIFT (Scale-Invariant Feature Transform) or SURF(Speeded Up Robust Features), and transforms the slice plane projectionimages TGi such that the detected feature points agree among them, tothereby correct the positional misalignment. Thus, the positionalmisalignment between the slice plane projection images TGi is corrected,as shown in FIG. 18, and the distributions of pixel values of the sliceplane projection images TGi substantially agree with one another.

It should be noted that the SIFT is a technique that describes featurequantities which are invariant to rotation and/or scaling of an image atfeature points, and aligns the positions of a plurality of images basedon the described feature quantities. The SURF is a technique for morequickly achieving the above-described alignment by substituting theoperation performed in the SIFT with approximation. It should be notedthat the operation to correct positional misalignment performed in thisembodiment is not limited to the SIFT or SURF, and any other suitabletechnique may be used.

In the fifth embodiment, after the correction of the positionalmisalignment between the slice plane projection images TGi, the pixelvalue calculating unit 33 generates a tomographic image of the sliceplane Tj by calculating the pixel values on the slice plane Tj,similarly to the above-described embodiments.

As described above, in the fifth embodiment, positional misalignmentbetween the slice plane projection images TGi projected on the sliceplane Tj is corrected. Thus, the influence of a three-dimensionalmechanical error and a three-dimensional body motion can be handled onlyas a two-dimensional positional misalignment on the slice plane Tj. Thisallows effectively removing the positional misalignment due to amechanical error and a body motion on the slice plane Tj, therebyimproving the image quality of the tomographic image.

It should be noted that, in the tomographic images of adjacent sliceplanes, the corresponding pixel positions tend to have the same pixelvalue. For this reason, in the above-described embodiments, a pluralityof regression surfaces at a plurality of slice planes of the breast Mmay be generated, and the regression surface of a slice plane ofinterest may be smoothed using the regression surfaces of the adjacentslice planes. Specifically, for a regression surface of a slice planeTj, a correlation among pixel values at corresponding pixel positions onregression surfaces of three adjacent slice planes Tj−1, Tj, and Tj+1 iscalculated. Then, if the correlation exceeds a predetermined thresholdvalue, smoothing is performed for the pixel position on the slice planeTj by calculating an average of the pixel values of the three sliceplanes Tj−1, Tj, and Tj+1, for example. As the correlation, absolutedifference values between the pixel values at the corresponding pixelpositions can be used, for example. This allows taking the influence ofpixel values at adjacent slice planes into account, thereby allowinggeneration of a high image quality tomographic image with even reducednoise.

Further, after the regression surface is generated in theabove-described embodiments, the regression surface may be modified bycalculating an absolute difference value between each pixel valueprojected on each coordinate position on the slice plane Tj and thevalue of the regression surface at the corresponding coordinateposition, determining a pixel value whose absolute difference valueexceeds a predetermined threshold value as an outlier, and removing theoutlier or weighting the outlier with a small weight. For example, inthe case where the regression curve as shown in FIG. 8 is generated, anabsolute difference value between each of the five pixel valuesprojected on the rightmost pixel position on the slice plane Tj and thevalue of the regression curve at the corresponding pixel position iscalculated. In this case, the absolute difference values of the twopixel values having the large values exceed the threshold value. Then,the two pixels having the large values are removed as outliers orweighted with a small weight to modify the regression curve. This allowsgenerating a regression curve, as shown in FIG. 9, where the value atthe pixel position including the outliers does not largely differ fromthe value at the adjacent pixel position.

Further, while the regression surface is generated after all the pixelvalues of the projection images Gi are projected on the slice plane Tjin the above-described embodiments, the regression surface may begenerated for each projection image Gi. In this case, a correlation atcorresponding coordinate positions among the regression surfacescalculated for the individual projection images Gi is calculated. As thecorrelation, absolute difference values can be used. Then, if there is aregression surface having a small correlation, i.e., having a pixelvalue whose absolute difference value exceeds a predetermined thresholdvalue, the pixel value of the regression surface at the coordinateposition with the small correlation is determined as an outlier and isremoved or weighted with a small weight, and then a regression surfaceis generated based on pixel values of all the projection images Giprojected on coordinate positions on the slice plane Tj.

When the tomosynthesis imaging is performed, the amount of x-rayreaching the radiation detector 15 varies between when the x-rayorthogonally enters the radiation detector 15 and when the x-rayobliquely enters the radiation detector 15, and the image quality of theprojection images Gi varies depending on the radiation source positionwith which each projection image Gi is taken. Specifically, comparing aprojection image that is obtained when the x-ray orthogonally enters theradiation detector 15 with a projection image that is obtained when thex-ray obliquely enters the radiation detector 15, the latter has a lowerdensity and thus is whiter due to a smaller amount of radiation reachingthe radiation detector 15. Further, there may be density irregularityamong the projection images due to influence of characteristics of theradiographic imaging apparatus, etc. It is therefore preferred toproject the pixel values of the projection images Gi on coordinatepositions on the slice plane Tj after the variation of image quality andthe density irregularity among the projection images Gi are corrected.

The variation of density based on the amount of radiation reaching thedetector and the density irregularity are included in low frequencycomponents of the projection images Gi. It should be noted that the lowfrequency refers to frequencies that are appropriately set to be 50% orless of the Nyquist frequency, which is determined by the spacingbetween the pixel positions of the projection images Gi. It is thereforepreferred to remove the low frequency components from the projectionimages Gi and project the pixel values of the projection images Gi fromwhich the low frequency components are removed on coordinate positionson the slice plane Tj. This allows correcting the variation of imagequality among the projection images Gi, thereby allowing generation of atomographic image with even higher image quality. The removal of the lowfrequency components can be achieved by performing frequencydecomposition on the projection images, for example, to calculate thelow frequency components, and subtract the calculated low frequencycomponents from the projection images. Alternatively, the removal of thelow frequency components may be achieved by generating a blurred imageof each projection image, and subtracting the blurred image from theprojection image.

Further, in the above-described embodiments, the process to generate theregression surface may be sequentially iterated. For example, in theabove-described method for calculating the regression surface using theweighted least squares method, after the regression surface isgenerated, the weight wk for each observation point uk is calculatedaccording to the equation (8) below, where f(uk) is the value of thecalculated regression curve at the observation point uk:

wk=e ^(−(qk−f(uk))) ²   (8)

According to the equation (8), a smaller value of the weight k iscalculated for a larger difference between each observed value qk andthe value of the regression curve at the observation point uk. Then,when a regression curve is generated according to the equation (4) aboveusing the thus calculated weights wk, influence of values that arelargely different from the previously generated regression curve isreduced in the newly generated regression curve. In particular, if thereare outliers, the outliers are weighted with smaller weights, therebyreducing artifacts at pixel positions of the outliers in a generatedtomographic image. It should be noted that the number of iterations ofthe process to generate the regression surface may be set in advance, orthe process to generate the regression surface may be iterated until apredetermined convergence condition is satisfied. The convergencecondition may, for example, be that the difference, i.e., the value ofqk−f(uk), resulting from the iterative calculation is not greater than athreshold value.

It should be noted that the process to generate the regression surfacemay be sequentially iterated also in the case where the regression curveis generated using the moving average method or using a kernel function.In the case where the moving average method is used, the weight for eachobservation point uk may be calculated similarly to the equation (8)above, and calculation of the weighted moving average may be iterated.In the case where the technique using a kernel function is used, a termfor calculating the weight wk, as shown by the equation (8), may becombined into the equation for determining the kernel function, and theregression curve may be generated by iterating the technique using thekernel function.

While the tomographic image is generated by generating the regressionsurface by the pixel value calculating unit 33 in the above-describedembodiments, the tomographic image may be generated by calculating thepixel values at the pixel positions on the slice plane Tj by regressionanalysis, without generating a regression surface. In this case, thesampling interval of the tomographic image to be generated is set inadvance, and each coordinate position corresponding to the samplinginterval is set as the pixel position of interest on the slice plane Tjto calculate the pixel value at the pixel position of interest by theregression analysis.

Further, while the subject of the tomosynthesis imaging in theabove-described embodiments is the breast M, the disclosure is alsoapplicable to tomosynthesis imaging with a subject other than a breast.

While only the x-ray source 16 is moved in the above-describedembodiments, some imaging apparatuses allow moving the x-ray source 16and the radiation detector 15 synchronously with each other. In thiscase, the x-ray source 16 and the radiation detector 15 may be movedsynchronously with each other. Alternatively, the x-ray source 16 may befixed and only the radiation detector 15 may be moved.

While the disclosure is applied to an imaging apparatus that performstomosynthesis imaging in the above-described embodiments, the disclosureis applicable to any imaging apparatus that obtains a plurality ofprojection images by imaging a subject with different radiation sourcepositions. For example, the disclosure is applicable to a CT imagingapparatus, where the radiation source and the radiation detector aredisposed to face each other with the subject being the center, and theset of the radiation source and the radiation detector is rotated aroundthe subject to obtain a plurality of projection images while applyingradiation from different angles.

While the trajectory of the x-ray source 16 is a circular arc in theabove-described embodiments, the trajectory of the x-ray source 16 maybe a straight line.

Now, advantageous effects of the embodiments of the disclosure aredescribed.

In the case where, for each of the different radiation source positions,pixel values at pixel positions on the corresponding projection image onstraight lines that connect the radiation source and the individualpixel positions on the projection image are projected as pixel values atcoordinate positions on the slice plane at which the slice planeintersects with the straight lines, it is not necessary to performinterpolation of the pixel values when the pixel values are projected.This allows generating a tomographic image with even higher imagequality. In particular, since the pixel values are also projected oncoordinate positions on the slice plane that are different fromcoordinate positions corresponding to pixel positions of the tomographicimage, a high resolution and high image quality tomographic image can begenerated.

In the case where the pixel values at the pixel positions on the sliceplane are calculated by performing the regression analysis to generate aregression surface that represents a tomographic image of the sliceplane, and sampling the regression surface at a desired samplinginterval, a tomographic image with a desired resolution can begenerated.

Further, when the regression analysis is performed, changing thesharpness of the pixel value at the coordinate position of interestallows emphasizing the sharpness of the pixel value at the coordinateposition of interest or reducing the sharpness to achieve smoothing tosuppress noise. This allows generating a tomographic image having adesired image quality.

In the case where the level of change of the sharpness is changeddepending on information about at least one of the imaging conditionsunder which the projection images are taken and a structure of thesubject included in the projection images, a tomographic image having adesired image quality depending on at least one of the imagingconditions and the structure of the subject can be generated.

In the case where the pixel value at the coordinate position of interestis calculated with removing an outlier pixel value among pixel values ofthe projection images projected in a predetermined range relative to thecoordinate position of interest or weighting the outlier pixel valuewith a small weight, influence of the pixel value which is highlypossible to be an artifact can be reduced, thereby allowing generationof a tomographic image with even higher image quality.

It should be noted that the difference of the radiation source positionmay cause low frequency irregularity among the projection images. Inthis case, influence of the low frequency irregularity can be reduced byremoving the low frequency components of the projection images, andprojecting pixel values of the projection images from which the lowfrequency components are removed on coordinate positions on the sliceplane, thereby allowing generation of a tomographic image with evenhigher image quality.

The radiation emitted from the radiation source is a cone beam, whichspreads as it travels away from the radiation source. Since the positionof the surface of the detecting unit, at which the projection images areobtained, is farther from the radiation source than the slice plane, thetwo-dimensional coordinate position of a structure included in thesubject in each projection image differs from the position of thestructure in the tomographic image of the slice plane.

In this case, the two-dimensional coordinate position of the structureincluded in the subject in the tomographic image can be made agree withthe two-dimensional coordinate position of the structure in theprojection image obtained with a certain radiation source position bycorrecting the coordinate position on the slice plane on which the pixelvalue at each coordinate position of interest is projected based on thepositional relationship between the certain radiation source positionand the coordinate position of interest, such that the two-dimensionalcoordinates of the coordinate position of interest on the projectionimage obtained with the certain radiation source position agrees withthe two-dimensional coordinates of the coordinate position on the sliceplane on which the pixel value at the coordinate position of interest isprojected, and projecting the pixel values of the projection images onthe corrected coordinate positions on the slice plane.

In this case, when a radiographic image is obtained by imaging thesubject with the certain radiation source position, a tomographic imageis generated by calculating the pixel value at each coordinate positionof interest on the slice plane with the pixel values of the projectionimages being projected on the corrected coordinate positions, and theradiographic image and the tomographic image are displayed, thetwo-dimensional coordinate position of a structure included in thesubject in the displayed radiographic image agrees with thetwo-dimensional coordinate position of the structure in the displayedtomographic image. This allows more appropriate diagnosis.

In the case where a plurality of tomographic images at a plurality ofslice planes of the subject are generated, and an addition tomographicimage is generated by adding up the tomographic images, a pseudotransmission image having even higher image quality can be generated.

What is claimed is:
 1. A tomographic image generation device comprising:an image obtaining unit for obtaining a plurality of projection imagescorresponding to different radiation source positions, the projectionimages being taken by moving a radiation source relative to a detectingunit and applying radiation to a subject from the different radiationsource positions to which the radiation source is moved; a pixel valueprojecting unit for projecting pixel values of the projection images oncoordinate positions on a desired slice plane of the subject based on apositional relationship between the radiation source position with whicheach of the projection images is taken and the detecting unit, whilepreserving the pixel values of the projection images; and a pixel valuecalculating unit for calculating a pixel value at each coordinateposition of interest on the slice plane based on a plurality of pixelvalues of the projection images projected in a predetermined rangerelative to the coordinate position of interest on the slice plane tothereby generate a tomographic image of the slice plane.
 2. Thetomographic image generation device as claimed in claim 1, wherein thepixel value projecting unit projects, for each of the differentradiation source positions, pixel values at coordinate positions on thecorresponding projection image intersecting with straight lines thatconnect the radiation source position and individual pixel positions onthe slice plane as pixel values at the pixel positions on the sliceplane on the straight lines.
 3. The tomographic image generation deviceas claimed in claim 1, wherein the pixel value projecting unit projects,for each of the different radiation source positions, pixel values atpixel positions on the corresponding projection image on straight linesthat connect the radiation source position and the individual pixelpositions on the projection image as pixel values at coordinatepositions on the slice plane intersecting with the straight lines. 4.The tomographic image generation device as claimed in claim 3, wherein aspacing between coordinate positions on the slice plane is smaller thana spacing between pixel positions on the slice plane.
 5. The tomographicimage generation device as claimed in claim 1, wherein the pixel valuecalculating unit calculates the pixel value at the coordinate positionof interest by performing regression analysis on pixel values of theprojection images projected on the slice plane.
 6. The tomographic imagegeneration device as claimed in claim 5, wherein the pixel valuecalculating unit calculates pixel values at pixel positions on the sliceplane by performing the regression analysis to generate a regressionsurface that represents a tomographic image of the slice plane, andsampling the regression surface at a desired sampling interval, tothereby generate the tomographic image.
 7. The tomographic imagegeneration device as claimed in claim 6, wherein the sampling intervalis different from a sampling interval of the projection images.
 8. Thetomographic image generation device as claimed in claim 6, wherein, ifan instruction to change the size of an area of interest in thetomographic image being displayed is received, the pixel valuecalculating unit generates a tomographic image of the area of interestwith changing the sampling interval of an area of the regression surfacecorresponding to the area of interest according to the instruction tochange.
 9. The tomographic image generation device as claimed in claim5, wherein the pixel value calculating unit changes sharpness of thepixel value at the coordinate position of interest when the regressionanalysis is performed.
 10. The tomographic image generation device asclaimed in claim 9, wherein the pixel value calculating unit changes alevel of change of the sharpness depending on information of at leastone of imaging conditions under which the projection images are takenand a structure of the subject included in the projection images. 11.The tomographic image generation device as claimed in claim 1, whereinthe pixel value calculating unit calculates the pixel value at thecoordinate position of interest with removing an outlier pixel valueamong the pixel values of the projection images projected in thepredetermined range relative to the coordinate position of interest orweighting the outlier pixel value with a small weight.
 12. Thetomographic image generation device as claimed in claim 1, wherein thepixel value projecting unit removes low frequency components of theprojection images, and projects pixel values of the projection imagesfrom which the low frequency components are removed on coordinatepositions on the slice plane.
 13. The tomographic image generationdevice as claimed in claim 1, wherein the pixel value projecting unitcorrects, based on a positional relationship between a certain radiationsource position and each coordinate position of interest on theprojection image corresponding to the certain radiation source position,a coordinate position on the slice plane on which a pixel value at thecoordinate position of interest on the projection image is projectedsuch that two-dimensional coordinates of the coordinate position ofinterest on the projection image agrees with two-dimensional coordinatesof the coordinate position on the slice plane on which the pixel valueat the coordinate position of interest on the projection image isprojected, and projects the pixel values of the projection images on thecorrected coordinate positions on the slice plane.
 14. The tomographicimage generation device as claimed in claim 13, wherein the imageobtaining unit obtains a radiographic image of the subject taken byapplying the radiation to the subject from the certain radiation sourceposition, the pixel value calculating unit generates the tomographicimage by calculating the pixel value at the coordinate position ofinterest on the slice plane with the pixel values of the projectionimages being projected on the corrected coordinate positions, and thetomographic image generation device further comprises a display unit fordisplaying the radiographic image and the tomographic image.
 15. Thetomographic image generation device as claimed in claim 1, wherein thepixel value projecting unit and the pixel value calculating unitgenerate the tomographic image for each of a plurality of slice planesof the subject, and the tomographic image generation device furthercomprises a pseudo image generating unit for generating a pseudo imagefrom the tomographic images.
 16. The tomographic image generation deviceas claimed in claim 1, wherein the pixel value calculating unitcalculates weighting factors based on a difference between the pixelvalue at the coordinate position of interest and a pixel value at acoordinate position of each projection image corresponding to thecoordinate position of interest, and calculates the pixel value at thecoordinate position of interest again based on the plurality of pixelvalues of the projection images and the weighting factors to calculate anew pixel value at the coordinate position of interest.
 17. Thetomographic image generation device as claimed in claim 16, wherein thepixel value calculating unit iterates calculating new weighting factorsusing the new pixel value at the coordinate position of interest, andcalculating a new pixel value at the coordinate position of interestagain based on the plurality of pixel values of the projection imagesand the new weighting factors.
 18. A tomographic image generation methodcomprising the steps of: obtaining a plurality of projection imagescorresponding to different radiation source positions, the projectionimages being taken by moving a radiation source relative to a detectingunit and applying radiation to a subject from the different radiationsource positions to which the radiation source is moved; projectingpixel values of the projection images on coordinate positions on adesired slice plane of the subject based on a positional relationshipbetween the radiation source position with which each of the projectionimages is taken and the detecting unit, while preserving the pixelvalues of the projection images; and calculating a pixel value at eachcoordinate position of interest on the slice plane based on a pluralityof pixel values of the projection images projected in a predeterminedrange relative to the coordinate position of interest on the slice planeto thereby generate a tomographic image of the slice plane.
 19. Anon-transitory recording medium containing a tomographic imagegeneration program for causing a computer to execute the steps of:obtaining a plurality of projection images corresponding to differentradiation source positions, the projection images being taken by movinga radiation source relative to a detecting unit and applying radiationto a subject from the different radiation source positions to which theradiation source is moved; projecting pixel values of the projectionimages on coordinate positions on a desired slice plane of the subjectbased on a positional relationship between the radiation source positionwith which each of the projection images is taken and the detectingunit, while preserving the pixel values of the projection images; andcalculating a pixel value at each coordinate position of interest on theslice plane based on a plurality of pixel values of the projectionimages projected in a predetermined range relative to the coordinateposition of interest on the slice plane to thereby generate atomographic image of the slice plane.